Who's hosting? PCs? The publisher? Dedicated PS4s?
The Xbox 360 and PS3 both used client hosted servers for most games, so that might not be terribly accurate.
Client hosted servers where someone is playing on the server is not a dedicated server. On a dedicated server nobody is playing on the server. It's dedicated to hosting games. It doesn't really matter if this dedicated server is a PS4 or PC.
The problem with XBox Live (and PS3) was not really the lag. Most of the time the lag was bearable. The problem was the host had an unfair and really really big advantage. When the host was bad or average it did not really matter. But when the host was a god player it made him like a god.
I know really quickly when i'm hosting the game on Halo. People can't kill me and all my head shots register like if i was playing an offline game. When i'm not hosting trying to headshot the host is like trying to win the Tour de france while not using any drug.